A study was done to compare the effectiveness of cognitive behavioral therapy (CBT) to dialectic behavior therapy (DBT) for treating anxiety related conditions. Scoring of effectiveness was done by participating therapists on a scale from 0 to 100. Of 23 cases under CBT, effectiveness had sample mean 58.775, sample standard deviation 11.564, and 5-number summary 6 | 47 | 61 | 68 | 77. Of 18 cases under DBT, effectiveness had sample mean 52.311, sample standard deviation 7.013, and 5-number summary 35 | 46 | 53 | 57 | 64.
a) Interval estimate: Find the point estimate of the difference in population means of effectiveness under each therapy. Find the standard error of this estimate. Find the margin of error for a 95% confidence interval of the difference in population means, and report the 95% confidence interval.
b) Use a two-sided hypothesis test on the claim that the two therapies differ in their effectiveness.
1. State hypotheses
2. State and assess the validity of the distribution assumptions
3. Calculate the test statistic
4. Calculate the p-value
5. Using a 0.05 significance level, do you reject the null hypothesis or not? What is this decision in the context of the problem?
c) Interpret the confidence interval in part (a). Describe the consistency or discrepancy between the confidence interval and the conclusion of the test. If there is a discrepancy, what caused it ?